Influence of the external conditions on transitionally rough favorable pressure gradient turbulent boundary layers

Abstract

Laser Doppler anemometry measurements are carried out in order to investigate the influences of the external conditions on a transitionally rough favorable pressure gradient turbulent boundary layer. The acquired data is normalized using the scalings obtained by the means of equilibrium similarity of the outer flow. The point at hand is to not only understand the interaction between the rough surface and the outer flow but also to include the external pressure gradient as the flow evolves in the streamwise direction. It is found that the velocity profiles show the effects of the upstream conditions imposed on the flow when normalized with the free-stream velocity. However, the profiles do collapse when normalized with U _∞ δ*/δ, demonstrating that this scaling absorbs the roughness effects and upstream conditions. An augmentation in the Reynolds stresses occurs with an increase in the roughness parameter and a decrease due to the external favorable pressure gradient. However, close to the wall, there is an increase due to the favorable pressure gradient while on the outer part of the boundary layer there is a decrease in magnitude due to this imposed effect. The near-wall peak of the ⟨ u ² ⟩ component is dampened by the surface roughness condition due to the destruction of the viscous sublayer. In addition, the shape of the profile in the inner region tends to flatten due to the surface roughness. The upstream wind-tunnel speed also plays an important role thus creating a Reynolds number dependence on the outer flow of the Reynolds stress components. Furthermore, through 11 consecutive downstream locations, the skin friction coefficient is obtained for smooth and rough favorable pressure gradient data. The skin friction shows dependencies on the Reynolds number, the roughness parameter, and the favorable pressure gradient condition in the transitionally rough regime; while for the fully rough regime, it becomes form drag and the dependencies are on the favorable pressure gradient and the Reynolds shear stress. The external condition effects are isolated with a fixed parameter comparison. Favorable pressure gradient effects slow down the growth of the boundary layer while the surface roughness promotes its growth.

Keywords:

• Turbulent boundary layers
• favorable pressure gradient
• surface roughness
• laser Doppler anemometry

Acknowledgements

This work was possible due to grants from the Office of Naval Research monitored by Dr. Ronald Joslin as well as the National Science Foundation—AGEP Program under Dr. Roosevelt Johnson.